SOLUTION: For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$. What is $\phi(5)$?

Question 1207613: For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(5)$?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

phi(5) = 4, which is obvious.

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: 4

Explanation

For any prime p, we have the following:
phi(p) = p-1

There are p-1 positive integers smaller than p that are relatively prime to p.
1, 2, 3, ..., p-2, p-1
This intuitively makes sense because all of these values are not factors of the prime p (well except for the trivial case 1)

Examples:
phi(7) = 6
phi(11) = 10

If we had some value not relatively prime to p, smaller than p, then it would mean p isn't prime.
For instance if 2 and p weren't relatively prime, then p = 2k and p is even. But at this point p is not prime.

Further Reading
https://mathworld.wolfram.com/TotientFunction.html
and
https://en.wikipedia.org/wiki/Euler%27s_totient_function

RELATED QUESTIONS
prove that for all positive integers n, sigma(2n) is greater than 2*sigma (n) (where... (answered by richard1234)
Let n be a positive integer, k the number of prime numbers less than or equal to n, and... (answered by richard1234)
For what positive integers n greater than or equal to 2 is... (answered by Edwin McCravy)
How many positive integers {{{ n }}} less than 2015 have the property that {{{ 1/3 + 1/n... (answered by Edwin McCravy)
How many positive integers have exactly 3 proper divisors, each of which is less than 50? (answered by Edwin McCravy,CarlosOrtiz)
How can I prove that for each positive integer n, the sum of the first n odd positive... (answered by tommyt3rd)
Let n be a positive integer greater than 1. We call n prime if the only positive integers (answered by jim_thompson5910)
Let n be a positive integer and 0, t<0, FX(t)=⌊t⌋, 0≤t (answered by ikleyn)
Let n be a positive integer and 0, t<0, FX(t)=t/n , 0≤t (answered by ikleyn)